## Basics of ternary phase diagrams

Three-component phase diagrams can be equilateral triangles. Remember the phase rule ( F=C+2-P): there are too many degrees of freedom for a two-dimensional plot. This triangle is a section cut from a three-dimensional figure. Observe the sketch:

At any point in the triangle, the distances to A, B, and C must add up to 1.0. Along the line connecting A and C, B must be zero. At any apex, one component is 1.0 while both others are zero. Note the numbers on the sides leaving the apex for C. The fraction of C must decrease both along the line toward A and the line toward B. The following applet lets you select a point and read the concentrations of A, B, and C. Please be prepared to do this by hand on a quiz.

**The following is in terms understandable by those who have studied physical chemistry.**
In the context of solvent extraction, the possibilities are one phase in which the solvents are miscible or two liquid phases. For just one phase, F=3+2-1, or four degrees of freedom. One degree goes to fix the temperature or pressure, another for taking a slice from the three-dimensional diagram, and the remaining two degrees mean that one phase takes an area of the two-dimensional plot. When two liquid phases exist, F=3+2-2. Now there is one remaining degree of freedom; this is a line on the two-dimensional plot extending from the composition of one of the immiscible liquids to the composition of the other immiscible liquid. These lines define an envelope in which any point is a composition that must split into the two compositions of the two liquid phases. There will be a point where the line constricts to a point known as the plait point.

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*while on sabbatical leave, ESB, Porto, Portugal July 1996
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Java applet, Nov. 3, 1997